3x^2+6x=89

Solution for 3x^2+6x=89 equation:

3x^2+6x=89

We move all terms to the left:

3x^2+6x-(89)=0

a = 3; b = 6; c = -89;
Δ = b2-4ac
Δ = 62-4·3·(-89)
Δ = 1104
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{69}}{2*3}=\frac{-6-4\sqrt{69}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{69}}{2*3}=\frac{-6+4\sqrt{69}}{6}
$